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### ENGN 8101Modelling and Optimisation

Professor Qinghua Qin

Email :Qinghua.Qin@anu.edu.au

Tel: 6125 8274

Office: Room R228 Ian Ross Building

MODELLING OF ENGINEERING SYSTEMS

Engineering?

“Profession in which knowledge of maths & natural science gained by study and practice is used with judgment to develop ways to utilise economically, material and forces of nature for the benefit of mankind”

Definition by : ABET

ENGN8101 Modelling and Optimization

“Process of converting customer requirements into detailed plans (drawings and specifications) from which the product, process or system can be put together”

Product/process/system must meet all customer requirements and be best with respect to chosen goodness measure(s).

ENGN8101 Modelling and Optimization

Selecting the “best” design within the available means

What is our criterion for “best”design? Objective function

What are the available means? Constraints (design requirements)

How do we describe different designs? Design Variables

ENGN8101 Modelling and Optimization

Minimise

f(x); f l; x nObjectives

Subject to :

h(x) = 0; h m Equality Constraints

g(x) 0; g p Inequality constraints

xL x xUSide constraints

ENGN8101 Modelling and Optimization

Heuristic?

Objective?

Optimum design?

Generic Approach

- Choose an initial design
- Identify design variables, X
- Assign values to X
- Assess system for acceptance
- Modify X to improve design
- Iterate till design is acceptable

ENGN8101 Modelling and Optimization

Issues?

- Problem statement. Identify
- Design variables
- Constraints
- Objectives
- Choose validated analysis for function evaluation
- Optimization
- Solution procedure: Golden Section Method/ Conjugate Gradient Method…
- Sensitivity
- Surrogate building
- Software integration

ENGN8101 Modelling and Optimization

System engineering in PracticeDesign of Boeing 777

- Program launched in Oct 29,1990
- First flight on June 1994
- 777 has 132,500 engineered, unique parts and a total of three million+ total parts

ENGN8101 Modelling and Optimization

System engineering in practice

Design of the Boeing 777

- Program launched in
- October 29, 1990
- First flight on June
- 1994
- 777 has 132,500
- engineered, unique
- parts and a total of
- three million + total
- parts

ENGN8101 Modelling and Optimization

Text Books

- “Optimization concepts and applications in engineering”- A.D. Belegundu & T.R. Chandrupatla - Required
- “Engineering Methods for Robust Product Design” – W.Y. Fowlkes & C. M. Creveling – Strongly Recommeded
- Available at ANU Bookshop

ENGN8101 Modelling and Optimization

Assessment

- Problem sets(20%)
- modelling and optimization problems
- EXTEND DES + design assignment – 20%
- Experimental design exercise – 20%
- Final Exam(40%)

ENGN8101 Modelling and Optimization

- Every student to master all fundamental concepts
- You must spend time with the material
- It will be worth it in the future!
- I promise to do my best to provide a robust learning environment

ENGN8101 Modelling and Optimization

- Personal and corporate integrity is an essential element of any quality organization. Accordingly, I expect every student to avoid even the appearance of cheating, and to claim credit only for his or her own work.
- I promise the same level of personal integrity that I expect. Cheating of any kind simply will not be tolerated!

ENGN8101 Modelling and Optimization

MODELLING OF ENGINEERING SYSTEMS

“Real phenomena that are subject to uncertainty can be modelled using the language of probability. This model can be parameterized using real data with predictive behaviour subsequently generated”

Barry Nelson 1995

i.e. whose state varies with time

i.e. dynamic phenomena

e.g. an engineering system

What is a system?

- not for now!

ENGN8101 Modelling and Optimization

“Real phenomena that are subject to uncertainty can be modelled using the language of probability. This model can be parameterized using real data with predictive behaviour subsequently generated”

i.e. convert system into smaller entities whose state can be modelled using a probability distribution

e.g. what is the probability that after an hour, a machine is still working?

ENGN8101 Modelling and Optimization

“Real phenomena that are subject to uncertaintycan be modelled using the language of probability. This model can be parameterized using real data with predictive behaviour subsequently generated”

Take actual readings of variables and plug them into the probabilistic model to generate key performance characteristics

ENGN8101 Modelling and Optimization

“Real phenomena that are subject to uncertaintycan be modelled using the language of probability. This model can be parameterized using real data with predictive behaviour subsequently generated”

come up with statistically robust estimates of future system behaviour

ENGN8101 Modelling and Optimization

“Investigate how parametric design affects key parts of the system”

i.e. obtain combinations of parameters that give maximum desirability in a key performance measure

i.e. OPTIMIZATION

ENGN8101 Modelling and Optimization

Take a system and use modelling and optimization techniques to present a theoretically robust design

NEVER design using trial and error!

ENGN8101 Modelling and Optimization

Probability that a light bulb breaks

States = ‘working’ or ‘not working’ over a time ‘x’

When x=0 + δx – the light bulb has just been switched on

Can be modelled as an exponential distribution

Often used in failure analysis

Light bulb most likely to fail when switched on!

ENGN8101 Modelling and Optimization

“to deduce statements about the performance of a real or conceptual engineering system”

i.e.

Dynamic systems that are subject to uncertainty

Models = 100% predictable

Systems = never!

ENGN8101 Modelling and Optimization

Key to successful modelling of a system….

Scale down into manageable entities then model behaviour through probabilistic/statistical techniques

i.e. Discrete Event Modelling

An example of numerical modelling

ENGN8101 Modelling and Optimization

EXTEND – typical DE modelling software

ENGN8101 Modelling and Optimization

Also – simple analytical modelling

i.e. analytical solutions to linear, differential and partial differential equations

ENGN8101 Modelling and Optimization

Also - Structural/Numerical Modelling

ENGN8101 Modelling and Optimization

- Most analytical and numerical models tend to be discipline
- specific (exceptions include multi-body physics models)
- Some of these modelling techniques need expert training
- There are several practical applications where
- analytical/numerical modelling techniques are not effective
- (cost, time, expert training or limitations in coping with the
- complexity of the problem)

ENGN8101 Modelling and Optimization

How to model and thus optimize an engineering system to improve it

‘Improve’ could mean ‘enhance the quality of the output’

In terms of quality –

Possible to model a system without formally optimizing it

Also – may have to optimize a system without a model

Data generation not always possible

ENGN8101 Modelling and Optimization

Special note on Taguchi Methods

- These are methods that use quality as a performance measure
- They are not limited to any specific discipline area
- Often used when analytical and numerical modelling are ineffective
- Often used in synergy with other modelling strategies
- Widely used in industrial settings
- More like a philosophy than a technique

ENGN8101 Modelling and Optimization

- Introduction
- Discrete Event Modelling
- Review of the nature of statistics
- Basic probability
- Statistical models in simulation
- Modelling of queueing processes
- Quality Engineering
- Introduction to quality engineering
- Design of experiments (orthogonals, factorial, interactions)
- Parametric design (S/N ratios, 2-step optimization)
- Importance of loss functions
- Classical Optimization
- Philosophical issues
- Mathematical foundations
- Unconstrained optimization
- Constrained optimization

ENGN8101 Modelling and Optimization

- What is “best”?
- Which option “best”?
- 100% of the time? – neither will be!

Dynamic system with variables (customer type etc.)

One option best x% of the time

One option best y% of the time

If x»y – find the first option and live with the uncertainty

Uncertainty = randomness = stochastic

ENGN8101 Modelling and Optimization

Essential first step…… collect data!

What is this data giving us?

CASE STUDY 1

The general office of a large company has as one of its responsibilities, the photocopying area. Currently, they have one photocopying machine and one operator. Employees needing some copying work wait in a single line until called by the operator. Some jobs involve mere copying, whereas others are more complicated, requiring collation, stapling etc.

Employees are now complaining that they are waiting too long, so the office is considering expanding its photocopying service. There are two options. The first is to purchase another copier and a second operator, and the second option is to have a second copier for self-service jobs only (i.e. no operator). Which option is best?

To assist with the task, the following data were collected on one morning period:

ENGN8101 Modelling and Optimization

Or in a more meaningful structure……

i.e. a queueing scenario

a very common system model

ENGN8101 Modelling and Optimization

Data presentation methods…..Histogram

- Graphically visualize the data spread and hint at any pattern
- Divide data set into classes (ranges of values)
- sample size = n – no. of classes = √n

i.e. 100 observations of the inside diameter of a metal sleeve

20 samples of 5 specimens

To create a histogram…

ENGN8101 Modelling and Optimization

49.90 49.92 49.94 49.96 49.98 50.00 50.02 50.04 50.06 50.08 50.10

ENGN8101 Modelling and Optimization

- Look at the average service times: full service = 7
- self service = 3
- all service = 4.6
- problem? make second copier a self-service?
- - not yet!
- Service time = wrong variable to base decisions on
- most likely – 2nd copier will have no effect on service times

Need to differentiate between

variables under the customer’s control &

variables under the company’s control

Uncontrollable v. controllable factors!

ENGN8101 Modelling and Optimization

More appropriate to use a controllable factor

- e.g. delay (time waiting in queue)
- data – lead to sample paths
- 2 parts:
- Customer characteristics (arrival times, service times)
- Company characteristics (one-at-a-time, FCFS)
- =system inputsb) =system logic
- Concentrate on logic – not inputs

CASE STUDY 1

ENGN8101 Modelling and Optimization

Sample path method – a graphical system model

SAMPLE PATH – record of the time-dependent behaviour

of a system

SAMPLE PATH DECOMPOSITION – represents a sample path

as inputs and logic

SIMULATION – generates new sample paths without building

a new system

SAMPLE PATH ANALYSIS – extracts system performance

measures from sample paths

ENGN8101 Modelling and Optimization

Full-service + self-service 2 x Full-service

Self-service system: - define the system logic…

2 queues – 1 for full-service, 1 for self-service

no swapping of queues

Customers always join appropriate queue

Service times – same as before (uncontrollable (noise) factor

ENGN8101 Modelling and Optimization

Performance measure – waiting time

i.e. Delay

3 system events:

- customer arrival
- customer finish (full-service)
- customer finish (self-service)

CASE STUDY 1

Now – let’s run a simulation

based on the previous data…..

ENGN8101 Modelling and Optimization

system starts customer 1 arrives

customer 2 arrives customer 2 finishes etc…

ENGN8101 Modelling and Optimization

Continue this analysis on the sheets on the table

– then answer the following:

The first non-zero delay is at t = ?

It occurs for customer number ?

It is a delay of ? minutes

At t = ? two events occur simultaneously

The simulation ends at t = ?

Which customers experience delays?

How big are these delays?

answers

45

7

1

76

129

7&13

1&7

ENGN8101 Modelling and Optimization

Continue this analysis on the sheets on the table

– then answer the following:

The first non-zero delay is at t =45

It occurs for customer number7

It is a delay of1minutes

At t =76two events occur simultaneously

The simulation ends at t =129

Which customers experience delays?7&13

How big are these delays1&7

ENGN8101 Modelling and Optimization

How does this compare to the alternative?

i.e. 2 copiers, both full-service

System logic:

1 queue – service delivered as FCFS

3 system events:

- customer arrival
- customer finish (left-hand machine)
- customer finish (right-hand machine)
- i.e.

ENGN8101 Modelling and Optimization

RESULTS (do it for yourself…?)

1 2

Simulation end time 129 124

Delayed customers 7,13 7,13,20

Delays 1,7 1,5,1

Total delay 8 7

Not much in it – but second model appears quicker

Unexpected??

Need to consider the “goodness” of the data set (the sample )

ENGN8101 Modelling and Optimization

Must ensure the data is reliable

i.e. statistically realistic and representative

Sample size?

Sample time? etc..

The statistics of sampling – sampling theory

Also –

relationship between sample and population

ENGN8101 Modelling and Optimization

- Predictive models provide an engineer with a quantitative understanding of a given problem
- They provide a means to trial multiple designs without full implementation (e.g. simulation)
- An engineer should know that a design will work before it is built

ENGN8101 Modelling and Optimization

- Determining good performance criteria is a key aspect of engineering a good system
- Quantitative performance criteria provide a means to measure performance of a system against the design goals
- Once performance criteria can be specified then the system design can be modified to optimize these criteria
- An engineer should design systems that optimize sensible and practical performance criteria

ENGN8101 Modelling and Optimization

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